Question

The product of three consecutive number in g.P is 216 and the sum of their squares is 133 find the numbers

Answer 1

Answer:

4 , 6 & 9

or

- 4 , 6 & -9

Step-by-step explanation:

let say three numbers are

a/r  , a  & ar

Product = a^3 = 216

so a =6

36/r^2 + 36 + 36r^2 = 133

1/r^2 + r^2 = 97/36   - eqA

(1/r + r)^2 - 2 = 97/36     from eq A

(1/r + r)^2 = 169/36

1/r + r = +/-  13/6

(1/r -r)^2 +2 = 97/36     from eq A

(1/r -r )^2 = 25/36

1/r - r = +/-  5/6

2r = 8/6

r = 4/6 = 2/3

three numbers are

9 , 6 , 4

2r = 18/6 = 3 so r = 3/2

numbers are

4 , 6 & 9

2r = - 18/6 = -3 => r = -3/2

so numbers are

-4  , 6 & -9

2r = -8/6 = -4/3 so r = -2/3

so numbers are

-9 , 6 & -4